Implicit finite difference methods on composite grids

Water hammer simulation by explicit central finite difference methods in staggered grids

Four explicit finite difference schemes, including Lax-Friedrichs, Nessyahu-Tadmor, Lax-Wendroff and Lax-Wendroff with a nonlinear filter are applied to solve water hammer equations. The schemes solve the equations in a reservoir-pipe-valve with an instantaneous and gradual closure of the valve boundary. The computational results are compared with those of the method of characteristics (MOC), a...

Implicit Finite Difference Methods for Hyperbolic Conservation Laws

Hyperbolic conservation laws (HCLs) are a class of partial differential equations that model transport processes. Many important phenomena in natural sciences are described by them. In this paper we consider finite difference methods for the approximation of HCLs. As HCLs describe an evolution in time, one may distinguish explicit and implicit schemes by the corresponding time integration mecha...

Composite Mesh Difference Methods

water hammer simulation by explicit central finite difference methods in staggered grids

four explicit finite difference schemes, including lax-friedrichs, nessyahu-tadmor, lax-wendroff and lax-wendroff with a nonlinear filter are applied to solve water hammer equations. the schemes solve the equations in a reservoir-pipe-valve with an instantaneous and gradual closure of the valve boundary. the computational results are compared with those of the method of characteristics (moc), a...

Energy stable and high-order-accurate finite difference methods on staggered grids

For wave propagation over distances of many wavelengths, high-order finite difference methods on staggered grids are widely used due to their excellent dispersion properties. However, the enforcement of boundary conditions in a stable manner and treatment of interface problems with discontinuous coefficients usually pose many challenges. In this work, we construct a provably stable and high-ord...